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Teoriya Veroyatnostei i ee Primeneniya, 2008, Volume 53, Issue 2, Pages 382–390
DOI: https://doi.org/10.4213/tvp2421 (Mi tvp2421) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Short Communications

On Gaussian Measure of Balls in a Hilbert Space

L. V. Rozovskii

Saint-Petersburg Chemical-Pharmaceutical Academy
Full-text PDF (936 kB) Citations (5)
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DOI: https://doi.org/10.4213/tvp2421
Abstract: Let $X$ be a centered Gaussian random vector taking values in a separable Hilbert space $H$, and let $a\in H$. We investigate the behavior of the density and the distribution function of a noncentered ball $\|X-a\|^2$ by means of its Laplace transform and obtain the results with an optimal estimate of the accuracy rate. As a tool we use a “local limit theorems” approach.
Keywords: small balls, Gaussian measure, Hilbert space, Laplace transform.
Received: 21.10.2003
Revised: 14.02.2008
English version:
Theory of Probability and its Applications, 2009, Volume 53, Issue 2, Pages 357–364
DOI: https://doi.org/10.1137/S0040585X97983638
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: L. V. Rozovskii, “On Gaussian Measure of Balls in a Hilbert Space”, Teor. Veroyatnost. i Primenen., 53:2 (2008), 382–390; Theory Probab. Appl., 53:2 (2009), 357–364
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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